[10] A 3/1 hybrid ARM for $424,000 is to be made for 15 years with an initial pe

Question

[10] A 3/1 hybrid ARM for $424,000 is to be made for 15 years with an initial period MEY of 4%. The index is the 1-year CMT and the margin is 200bps. Interest rate caps are 2/6/3 (last cap is for the fixed-to-floating reset), and the payment cap is 20% with a 120% negative amortization cap. All payments are monthly and the mortgage is fully amortizing. Assume that the borrower never curtails the loan. 1. Also assume that the index on each anniversary of closing will be (date, index): (0,4%), (1,65%. (2,65%), (3,7%) (4,75%), (5-30, 6.5%) A. 12] What are the payments in year 1? B. (1] What is the OLB at the end of year 3? C. [1] What are the payments in year 4? D. [6] If upfront variable fees are 3% of loan amount, and fixed fees are S2,000, what is the APR that the lender must disclose to the borrower? 2. (10] A homeowner purchases a property for $900,000. He finances the purchase with an 809 LTV, 30-year fully amortizing GPM carrying a 7% interest rate. A 20% rate of graduation will applied to monthly payments beginning year 2 and the beginning of year 3, only (payments years 3 and 4 and on are the same). The homeowner will sell the property after 8 years and does not curtail the loan ever. Upfront fees amount to 4% of the loan amount, plus $4,000 which were financed. A prepayment penalty of 3% applies. What is the effective cost of the loan?

Explanation / Answer

Loan Amount =$424,000

Initial Index =4%

Margin =200bps

Initial Full Index Rate =4% +2% =6% or 0.5% monthly

Since the ARM is 3/1 => Interest remains fixed for first 3 years

A.) Payments in Year-1 =(0.005,180,424000) =$3,577.95

B.) From Loan Ammortization Table, loan outstanding balance after 3 years =$366,650

C.) Index in Year-3 =7% => Full Index Rate for Year-4=7%+2% =9%

As 9% is higher by 3% from the last year rate of 6% and there is periodic interest rate cap of 2%

=> Applicable Interest for Year-4 =6%+2% =8% or 0.67% monthly

Payment Cap=20% => Max. New Payment Possible =$3,577.95 x 1.20 =$4,293.54

Payment for Year-4 will be =PMT(0.0067,144,366650) =$3,968.81

4.) Initial Variable Cost =$0.03x424,000=$12,720

Initial Fixed Cost =$2,000

Index in Year-4 =7.50% => Full Index Rate for Year-5=7.50%+2% =9.50%

Loan Outstanding at the end of Year-4 =$347,670

As 9.50% is less than by 3% increase from the last year rate of 8% and there is periodic interest rate cap of 2%

=> Applicable Interest for Year-5 =9.50% or 0.79167% monthly

Payment Cap=20% => Max. New Payment Possible =$3,968.81 x 1.20 =$4,762.57

Payment for Year-5 will be =PMT(0.0079,132,347670) =$4,255.01

Index in Year-5 =6.50% => Full Index Rate for Year-6=6.50%+2% =8.50%

Loan Outstanding at the end of Year-5 =$328,832

As 8.50% is less than by 2% decrease from the last year rate of 9.50% and there is periodic interest rate cap of 2%

=> Applicable Interest for Year-6 =8.50% or 0.7083% monthly

Payment Cap=20% => Max. New Payment Possible =$4,255.01 x 1.20 =$5,106.12

Payment for Year-6 will be =PMT(0.007083,120,328832) =$4,077.05

Since, the index remains constant for the remaining life of the loan term, this payment will remain the same.

Let y be the quoted rate of interest,

424,000 = 12,720 + 2,000 + 3,577.95x{(1-(1+y)-36)/y} + 3,968.81x{(1-(1+y)-12)/y}x(1+y)-36 + 4,255.01x{(1-(1+y)-12)/y}x(1+y)-48 + 4,077.05x{(1-(1+y)-120)/y}x(1+y)-60'

424,000 = 12,720 + 2,000 + 3,577.95x{(1-(1+y)-36)/y} + 3,968.81x{(1-(1+y)-12)/y}x(1+y)-36 + 4,255.01x{(1-(1+y)-12)/y}x(1+y)-48 + 4,077.05x{(1-(1+y)-120)/y}x(1+y)-60'

409,280 = 3,577.95x{(1-(1+y)-36)/y} + 3,968.81x{(1-(1+y)-12)/y}x(1+y)-36 + 4,255.01x{(1-(1+y)-12)/y}x(1+y)-48 + 4,077.05x{(1-(1+y)-120)/y}x(1+y)-60'

Solving for y using trial and error method,

For y=0.006, RHS =432,422

For y=0.007, RHS =401,159

For y=0.0065, RHS =416,366

For y=0.00675, RHS =408,660

For y=0.006729, RHS =409,280

Hence, Annual Quoted rate is =0.006729*12 =0.08076 or 8.076%

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